Final answer:
The principal for $11,900 of interest at 6% for 50 days is calculated using the formula for ordinary interest. After adjusting for a 360-day year and rearranging the formula, the principal is found to be $1,428,000.00.
Step-by-step explanation:
To determine the principal for the interest earned, we use the formula Interest = Principal × rate × time, where interest is the amount earned, rate is the percent interest, and time is the period the money is invested or borrowed. Here, the interest is $11,900, the rate is 6% (or 0.06 as a decimal), and the time is 50 days. Since ordinary interest is assumed to be based on a 360-day year, we convert the time to a fraction of the year by dividing the number of days by 360.
The formula we use is rearranged to solve for the Principal: Principal = Interest / (rate × time). Time in years is 50/360, so:
Principal = $11,900 / (0.06 × (50/360))
Principal = $11,900 / (0.06 × 0.1389)
Principal = $11,900 / 0.008333
Principal = $1,428,000.00